Calculate the ratio of the magnitude of the electric force to the...

The electric force between two protons separated by a distance $r$ is given by Coulomb's law:

$F_{e} = \dfrac{1}{4\pi\epsilon_{0}} \dfrac{e^2}{r^2}$

The gravitational force between them is given by Newton's law of gravitation:

$F_{g} = G \dfrac{m_{p}^2}{r^2}$

The ratio of the electric force to the gravitational force is:

$\dfrac{F_{e}}{F_{g}} = \dfrac{e^2}{4\pi\epsilon_{0} G m_{p}^2}$

Substituting the standard values:
$e = 1.6 \times 10^{-19} \text{ C}$
$\dfrac{1}{4\pi\epsilon_{0}} = 9 \times 10^9 \text{ N m}^2\text{/C}^2$
$G = 6.67 \times 10^{-11} \text{ N m}^2\text{/kg}^2$
$m_{p} = 1.67 \times 10^{-27} \text{ kg}$

$\dfrac{F_{e}}{F_{g}} = \dfrac{9 \times 10^9 \times (1.6 \times 10^{-19})^2}{6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2}$

$\dfrac{F_{e}}{F_{g}} = \dfrac{9 \times 10^9 \times 2.56 \times 10^{-38}}{6.67 \times 10^{-11} \times 2.7889 \times 10^{-54}}$

$\dfrac{F_{e}}{F_{g}} = \dfrac{23.04 \times 10^{-29}}{18.60 \times 10^{-65}}$

$\dfrac{F_{e}}{F_{g}} \approx 1.24 \times 10^{36}$